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Simplifying 2z2 + -1(20 + 9i) * z + 50 = 0 Reorder the terms for easier multiplication: 2z2 + -1z(20 + 9i) + 50 = 0 2z2 + (20 * -1z + 9i * -1z) + 50 = 0 Reorder the terms: 2z2 + (-9iz + -20z) + 50 = 0 2z2 + (-9iz + -20z) + 50 = 0 Reorder the terms: 50 + -9iz + -20z + 2z2 = 0 Solving 50 + -9iz + -20z + 2z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -9iz + -20z + -50 + 2z2 = 0 + -50 Reorder the terms: 50 + -50 + -9iz + -20z + 2z2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -9iz + -20z + 2z2 = 0 + -50 -9iz + -20z + 2z2 = 0 + -50 Combine like terms: 0 + -50 = -50 -9iz + -20z + 2z2 = -50 Add '20z' to each side of the equation. -9iz + -20z + 20z + 2z2 = -50 + 20z Combine like terms: -20z + 20z = 0 -9iz + 0 + 2z2 = -50 + 20z -9iz + 2z2 = -50 + 20z Add '-2z2' to each side of the equation. -9iz + 2z2 + -2z2 = -50 + 20z + -2z2 Combine like terms: 2z2 + -2z2 = 0 -9iz + 0 = -50 + 20z + -2z2 -9iz = -50 + 20z + -2z2 Divide each side by '-9z'. i = 5.555555556z-1 + -2.222222222 + 0.2222222222z Simplifying i = 5.555555556z-1 + -2.222222222 + 0.2222222222z Reorder the terms: i = -2.222222222 + 5.555555556z-1 + 0.2222222222z
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